The phenomenon of particle creation within a resonantly vibrating lossy cavity is investigated for the example of a massless scalar field at finite temperature. Leakage is provided by insertion of a dispersive mirror into a larger ideal cavity. Via the rotating wave approximation we demonstrate that for the case of parametric resonance the exponential growth of the number of created particles and the strong enhancement at finite temperatures are preserved in the presence of reasonable losses. The relevance for experimental tests of quantum radiation via the dynamical Casimir effect is addressed.
The phenomenon of particle creation within an almost resonantly vibrating cavity with losses is investigated for the example of a massless scalar field at finite temperature. A leaky cavity is designed via the insertion of a dispersive mirror into a larger ideal cavity (the reservoir). In the case of parametric resonance the rotating wave approximation allows for the construction of an effective Hamiltonian. The number of produced particles is then calculated using response theory as well as a non-perturbative approach. In addition we study the associated master equation and briefly discuss th…
The minimum time required for a quantum system to evolve from an arbitrary initial state to its orthogonal state is known as the quantum speed limit (QSL) time. In this work, we consider the model in which a single qubit moves inside a leaky cavity and then we study the QSL time for this model. Notably, we show that for both weak and strong coupling regimes, the QSL time increases with increasing the velocity of the qubit inside the leaky cavity. Moreover, it is observed that by increasing qubit velocity, the speed of the evolution tends to a constant value and the system becomes more stable.
For the excitons in the quantum well placed within a leaky cavity, the quantum decoherence of a mesoscopically superposed states is investigated based on the factorization theory for quantum dissipation. It is found that the coherence of the exciton superposition states will decrease in an oscillating form when the cavity field interacting with the exciton is of the form of quasimode. The effect of the thermal cavity fields on the quantum decoherence of the superposition states of the exciton is studied and it is observed that the higher the temperature of the environment is, the shorter the d…
We consider first a system of two enatangled cavities and a single two-level atom passing through one of them. A ``monogamy'' inequality for this tripartite system is quantitatively studied and verified in the presence of cavity leakage. We next consider the simultaneous passage of two-level atoms through both the cavities. Entanglement swapping is observed between the two-cavity and the two-atom system. Cavity dissipation leads to the quantitative reduction of information transfer though preserving the basic swapping property.
An in-depth theoretical study is carried out to examine the quasi-deterministic entanglement of two atoms inside a leaky cavity. Two $Λ$-type three-level atoms, initially in their ground states, may become maximally entangled through the interaction with a single photon. By working out an exact analytic solution, we show that the probability of success depends crucially on the spectral function of the injected photon. With a cavity photon, one can generate a maximally entangled state with a certain probability that is always less than 50%. However, for an injected photon with a narrower spectr…
Uncertainty principle has a fundamental role in quantum theory. This principle states that it is not possible to measure two incompatible observers simultaneously. The uncertainty principle is expressed logically in terms of standard deviation of the measured observables. In quantum information it has been shown that the uncertainty principle can be expressed by means of Shannon's entropy. Entropic uncertainty relation can be improve by consider an additional particle as the quantum memory. In the presence of quantum memory the entropic uncertainty relation is called quantum memory assisted en…
In contrast to the free-space evolution of an atom governed by a multi-mode interaction with the surrounding electromagnetic vacuum, the evolution of a cavity-QED system can be characterized by just three parameters, (i) atom-cavity coupling strength g, (ii) cavity relaxation rate κ, and (iii) atomic decay rate into the non-cavity modes γ. In the case of an atom inserted into a planar resonator with an input beam coupled from the outside, it has been shown by Koshino [Phys. Rev. A 73, 053814 (2006)] that these three parameters are determined not only by the atom and cavity characteristics, but…
The resonant scalar particle generation for a swinging cavity resonator in the Casimir vacuum is examined. It is shown that the number of particles grows exponentially when the cavity rotates at some specific external frequency.
We obtain expressions for the Casimir energy and force following an approach which may be applied to cavities made up of arbitrary materials. In the case of planar cavities we obtain the well known Lifshitz formula. The approach is easily generalizable to other geometries.
We study analytically the photon generation from vacuum due to the Dynamical Casimir effect in a cavity with a two-level atom, prepared initially in an arbitrary pure state. Performing small unitary transformations we obtain closed analytical expressions for the probability amplitudes and other important quantities in the resonant/dispersive regimes.
Motivated by a recent proposal for an experimental verification of the dynamical Casimir effect, the macroscopic electromagnetic field within a perfect cavity containing a thin slab with a time-dependent dielectric permittivity is quantized in terms of the dual potentials. For the resonance case, the number of photons created out of the vacuum due to the dynamical Casimir effect is calculated for both polarizations (TE and TM). PACS: 42.50.Lc, 03.70.+k, 42.50.Dv, 42.60.Da.
Emphasizing first the utility of the generalized Fresnel coefficients in the theory of the Casimir effect in planar cavities, we complement our previous discussion of the ordinary Casimir force on and the Casimir stress in a metal (plasma) slab in a planar cavity. We demonstrate strong dependence of the Casimir stress in a thin slab on properties of the bounding medium in the symmetric Lifshitz configuration. Contrary to this, the stress in a thick slab gradually becomes insensitive on external boundary conditions. We also consider the position dependence of the Casimir force on and stress in …
Vacuum fluctuations produce a force acting on a rigid Casimir cavity in a weak gravitational field. Such a force is here evaluated and is found to have opposite direction with respect to the gravitational acceleration; the order of magnitude for a multi-layer cavity configuration is analyzed and experimental detection is discussed, bearing in mind the current technological resources.
We discuss the possibility of verifying the equivalence principle for the zero-point energy of quantum electrodynamics, by evaluating the force, produced by vacuum fluctuations, acting on a rigid Casimir cavity in a weak gravitational field. The resulting force has opposite direction with respect to the gravitational acceleration; the order of magnitude for a multi-layer cavity configuration is derived and experimental feasibility is discussed, taking into account current technological resources.
An effective toy model for an ideal one-dimensional nonstationary cavity is taken to be the starting point to derive a fitting markovian master equation for the corresponding leaky cavity. In the regime where the generation of photons via the dynamical Casimir effect is bounded, the master equation thus constructed allows us to investigate the effects of decoherence on the average number of Casimir photons and their quantum fluctuations through the second-order correlation function.
We study analytically and numerically the dynamical Casimir effect in a cavity containing two stationary 2-level atoms that interact with the resonance field mode via the Tavis-Cummings Hamiltonian. We determine the modulation frequencies for which the field and atomic excitations are generated and study the corresponding dynamical behaviors in the absence of damping. It is shown that the two-atom setup allows for monitoring of photon generation without interrupting the growth, and different entangled states can be generated during the process.
In this paper we study an optomechnical system enclosed by an optical cavity with one mirror attached to a spring as a closed quantum system. We provide a different angle of studying the phenomenons related to the dynamical Casimir effect via Feynman diagram technique. Dressing effects of phonon, photon and coupling strength are discussed. The energy shift of ground state is obtained. The dynamical Casimir effect is modeled by the scattering processes converting phonons to photons and the corresponding scattering amplitudes are computed. The force-force correlation function of the radiation pr…
We study the photon generation from vacuum via the Dynamical Casimir Effect in a cavity containing a N-level detector in equally-spaced resonant ladder configuration or N-1 identical resonant two-level atoms. If the modulation frequency equals exactly twice the unperturbed cavity frequency, the photon growth goes on steadily for odd N, while for even N at most N-2 photons can be generated. This finding is corroborated by numerical calculations. In the limit $N\to\infty$ we obtain the harmonic oscillator model of the detector, which admits analytical results.
We extend our previous work on the electromagnetic Casimir-Lifshitz interaction between two bodies when one is contained within the other. We focus on the fluctuation-induced pressure acting on the cavity wall, which is assumed to be spherical. This pressure can be positive or negative depending on the response functions describing the bodies and the medium filling the cavity. However, we find that, under general hypotheses, the sign is independent of the geometry of the configuration. This result is based on the representation of the Casimir-Lifshitz energy in terms of transition operators. I…
We study the dynamical Casimir effect in the presence of a finite coherence time, which is associated with a finite quality factor of the optical cavity. We use the time refraction model, where a fixed cavity with a modulated optical medium, replaces the empty cavity with a vibrating mirror. Temporal coherence is described with the help of cavity quasi-mode operators. Asymptotic expressions for the number of photon pairs generated from vacuum are derived.
We study the dynamical Casimir effect in an electromagnetic cavity containing a Kerr medium. We obtain approximate expressions for the time evolution operator as well as for the number operator in the Heisenberg representation. We have found that the generation of photons from quantum vacuum is strongly affected by the presence of the Kerr medium, sharing physical features with the case of two two-level atoms in a cavity with oscillating walls. The nonlinear medium produces a saturation effect in the photon generation which shows strong oscillations whose frequency increases with the intensity…
We consider particle creation (the Dynamical Casimir effect) in a uniformly contracting ideal one-dimensional cavity non-perturbatively. The exact expression for the energy spectrum of created particles is obtained and its dependence on parameters of the problem is discussed. Unexpectedly, the number of created particles depends on the duration of the cavity contracting non-monotonously. This is explained by quantum interference of the events of particle creation which are taking place only at the moments of acceleration and deceleration of a boundary, while stable particle states exist (and t…
We theoretically propose and investigate a feasible experimental scheme for the realization of the dynamical Casimir effect (DCE) in a hybrid optomechanical cavity with a moving end mirror containing an interacting cigar-shaped Bose-Einstein condensate (BEC). We show that in the red-detuned regime of cavity optomechanics together with the weak optomechanical coupling limit by \textit{coherent} modulation of the \textit{s}-wave scattering frequency of the BEC and the mechanical spring coefficient of the mechanical oscillator (MO), the mechanical and atomic quantum vacuum fluctuations are parame…
We consider the out-of-thermal-equilibrium Casimir-Polder interaction between atoms of He$^*$, Na, Cs, and Rb and a cavity wall made of sapphire coated with a vanadium dioxide film which undergoes the dielectric-to-metal phase transition with increasing wall temperature. Numerical computations of the Casimir-Polder force and its gradient as the functions of atom-wall separation and wall temperature are made when the latter exceeds the temperature of the environment. The obtained results are compared with those in experiment on measuring the gradient of the Casimir-Polder force between $^{87}$R…
It was predicted some time ago that the cavity dynamical Casimir effect (generation of photons from the initial vacuum state in a cavity with moving walls) might be observed if a boundary vibrates at the double frequency of some selected cavity mode. However, to register the created photons one has to couple the cavity mode with some detector. Considering the harmonic oscillator model of a detector, we analyze how different coupling regimes can affect the statistics of the created quanta.
We develop a microscopic toy model for Cavity dynamical Casimir effect (DCE), namely, the photon generation from vacuum due to a nonstationary dielectric slab in a fixed single mode cavity. We represent the slab by $N\gg 1$ noninteracting two-level atoms coupled to the field via the standard dipole interaction. We show that the DCE is contained implicitly in the light-matter interaction Hamiltonian when its parameters are externally prescribed functions of time. We also predict several new phenomena, such as saturation of the photon growth due to effective Kerr nonlinearity, generation of pair…
We study the electromagnetic Casimir interaction of a compact object contained inside a closed cavity of another compact object. We express the interaction energy in terms of the objects' scattering matrices and translation matrices that relate the coordinate systems appropriate to each object. When the enclosing object is an otherwise empty metallic spherical shell, much larger than the internal object, and the two are sufficiently separated, the Casimir force can be expressed in terms of the static electric and magnetic multipole polarizabilities of the internal object, which is analogous to…
We present and investigate an analogue model for a controllable photon geberation via the dynamical Casimir effect (DCE) in a cavity containing a degenerate optical amplifier (OPA) which is pumed by an amplitude-modulated field. The time modulation of the pump field in the model OPA system is equivalent to a periodic modulation of the cavity length, which is responsible for the generation of the Casimir radiation. By taking into account the rapidly oscillating terms of the modulation frequency, the effects of the corresponding counter-rotating terms (CRTs) on the analogue Casimir radiation eme…
We emphasize and demonstrate that, besides using the usual recursion relations involving successive layers, generalized Fresnel coefficients of a multilayer can equivalently be calculated using the recursion relations involving stacks of layers, as introduced some time ago [M. S. Tomas, Phys. Rev. A 51, 2545 (1995)]. Moreover, since the definition of the generalized Fresnel coefficients employed does not imply properties of the stacks, these nonstandard recursion relations can be used to calculate Fresnel coefficients not only for local systems but also for a general multilayer consisting of v…
Quantum vacuum fluctuations are a direct manifestation of Heisenberg's uncertainty principle. The dynamical Casimir effect allows for the observation of these vacuum fluctuations by turning them into real, observable photons. However, the observation of this effect in a cavity QED experiment would require the rapid variation of the length of a cavity with relativistic velocities, a daunting challenge. Here, we propose a quantum simulation of the dynamical Casimir effect using an ion chain confined in a segmented ion trap. We derive a discrete model that enables us to map the dynamics of the mu…
The frequencies of transitions between hyperfine levels of ground-state atoms can be measured with exquisite precision using magnetic-resonance techniques. This makes hyperfine transitions ideal probes of QED effects originating from the interaction of atoms with the quantized electromagnetic field. One of the most remarkable effects predicted by QED is the Casimir-Polder shift experienced by the energy levels of atoms placed near one or more dielectric objects. Here we compute the Casimir-Polder shift and the width of hyperfine transitions between ground-state Zeeman sub-levels of an hydrogen…
We theoretically study the dynamical Casimir effect (DCE), i.e., parametric amplification of a quantum vacuum, in an optomechanical cavity interacting with a photonic crystal, which is considered to be an ideal system to study the microscopic dissipation effect on the DCE. Starting from a total Hamiltonian including the photonic band system as well as the optomechanical cavity, we have derived an effective Floquet-Liouvillian by applying the Floquet method and Brillouin-Wigner-Feshbach projection method. The microscopic dissipation effect is rigorously taken into account in terms of the energy…
We analyze the thermal Casimir-Polder potential experienced by a ground-state molecule in a planar cavity and investigate the prospects for using such a set-up for molecular guiding. The resonant atom-field interaction associated with this non-equilibrium situation manifests itself in oscillating, standing-wave components of the potential. While the respective potential wells are normally too shallow to be useful, they may be amplified by a highly reflecting cavity whose width equals a half-integer multiple of a particular molecular transition frequency. We find that with an ideal choice of mo…
A "microscopic" justification of the "symmetric damping" model of a quantum oscillator with time-dependent frequency and time-dependent damping is given. This model is used to predict results of experiments on simulating the dynamical Casimir effect in a cavity with a photo-excited semiconductor mirror. It is shown that the most general bilinear time-dependent coupling of a selected oscillator (field mode) to a bath of harmonic oscillators results in two equal friction coefficients for the both quadratures, provided all the coupling coefficients are proportional to a single arbitrary function …
An ultracold atom above a horizontal mirror experiences quantum reflection from the attractive Casimir-Polder interaction, which holds it against gravity and leads to quantum levitation states. We analyze this system by using a Liouville transformation of the Schrödinger equation and a Langer coordinate adapted to problems with a classical turning point. Reflection on the Casimir-Polder attractive well is replaced by reflection on a repulsive wall and the problem is then viewed as an ultracold atom trapped inside a cavity with gravity and Casimir-Polder potentials acting respectively as top an…
In this paper, we theoretically propose and investigate a feasible experimental scheme for realizing the dynamical Casimir effect (DCE) of phonons in an optomechanical setup formed by a ground-state precooled mechanical oscillator (MO) inside a Fabry-P{é}rot cavity, which is driven by an amplitude-modulated classical laser field in the dispersive (far-detuned) regime. The time modulation of the driving field leads to the parametric amplification of the mechanical vacuum fluctuations of the MO, which results in the generation of Casimir phonons over time scales longer than the cavity lifetime. …
In this work we investigate the dynamical Casimir effect in a nonideal cavity by deriving an effective Hamiltonian. We first compute a general expression for the average number of particle creation, applicable for any law of motion of the cavity boundary. We also compute a general expression for the linear entropy of an arbitrary state prepared in a selected mode, also applicable for any law of motion of the cavity boundary. As an application of our results we have analyzed both the average number of particle creation and linear entropy within a particular oscillatory motion of the cavity boun…
We report a theoretical study of the optical properties of a three-level emitter embedded in an optical cavity including the non-rotating wave terms of the light-matter interaction Hamiltonian. Rabi oscillations induced by a continuous wave drive laser are responsible for a periodic time-modulation of the effective cavity resonance, which results in a significant dynamical Casimir emission. A clear signature of the back-action effect of the dynamical Casimir emission onto the drive laser is visible as a sizable suppression of its absorption.
We want to study the Casimir effect for a single conducting microscopic cylindrical cavity. The mathematical technique is based on the Green function of the geometry of the inside of the cavity, and the integral regularization is based on the plasma frequency cutoff for real conductors. Using the symmetric electromagnetic energy-momentum tensor, in terms of four potential, the total Casimir energy for the inside of the Cavity is calculated. Neglecting the contribution of the external (outside of the cavity) Casimir energy based on the reason recently presented in [1], the forces experienced by…
We calculate the Casimir energy at spherical cavities within a host made up of an arbitrary material described by a possibly dispersive and lossy dielectric response. To that end, we add to the coherent optical response a contribution that takes account of the incoherent radiation emitted by the host in order to guarantee the detailed balance required to keep the system at thermodynamic equilibrium in the presence of dissipation. The resulting boundary conditions allow a conventional quantum mechanical treatment of the radiation within the cavity from which we obtain the contribution of the ca…
The moving-mirror problem is microscopically formulated without invoking the external boundary conditions. The moving mirrors are described by the quantized matter field interacting with the photon field, forming dynamical cavity polaritons: photons in the cavity are dressed by electrons in the moving mirrors. The effective Hamiltonian for the polariton is derived, and corrections to the results based on the external boundary conditions are discussed.
The Casimir-Polder and van der Waals interactions between an atom and a flat cavity wall are investigated under the influence of real conditions including the dynamic polarizability of the atom, actual conductivity of the wall material and nonzero temperature of the wall. The cases of different atoms near metal and dielectric walls are considered. It is shown that to obtain accurate results for the atom-wall interaction at short separations, one should use the complete tabulated optical data for the complex refractive index of the wall material and the accurate dynamic polarizability of an ato…
Electromagnetic cavity modes in photonic and plasmonic resonators offer rich and attractive regimes for tailoring the properties of light-matter interactions. Yet there is a disturbing lack of a precise definition for what constitutes a cavity mode, and as a result their mathematical properties remain largely unspecified. The lack of a definition is evidenced in part by the diverse nomenclature at use - "resonance", "leaky mode", "quasimode", to name but a few - suggesting that the dissipative nature of cavity modes somehow makes them different from other modes, but an explicit distinction is …
Invariant-based master equation applied to driven qutrit coupled to a bath and a leaky cavity
Homer L. Dodge Department of Physics and Astronomy, The University of Oklahoma（俄克拉荷马大学霍默·L·道奇物理与天文系）；Center for Quantum Research and Technology, The University of Oklahoma（俄克拉荷马大学量子研究与技术中心）；School of Electrical and Computer Engineering, The University of Oklahoma（俄克拉荷马大学电气与计算机工程学院）
We establish an explicit analogy between the dynamical Casimir effect and the photon emission of a thin non-linear crystal pumped inside a cavity. This allows us to propose a system based on a type-I optical parametric oscillator (OPO) to simulate a cavity oscillating in vacuum at optical frequencies. The resulting photon flux is expected to be more easily detectable than with a mechanical excitation of the mirrors. We conclude by comparing different theoretical predictions and suggest that our experimental proposal could help discriminate between them.
We consider the interaction pressure acting on the surface of a dielectric sphere enclosed within a magnetodielectric cavity. We determine the sign of this quantity regardless of the geometry of the cavity for systems at thermal equilibrium, extending the Dzyaloshinskii-Lifshitz-Pitaevskii result for homogeneous slabs. As in previous theorems regarding Casimir-Lifshitz forces, the result is based on the scattering formalism. In this case the proof follows from the variable phase approach of electromagnetic scattering. With this, we present configurations in which both the interaction and the s…
We develop a model of a quantum field confined within a cavity with a movable wall where the position of the wall is quantized. We obtain a full description of the dynamics of both the quantum field and the confining wall depending on the initial state of the whole system. Both the reaction and back-reaction of the field on the wall, and the wall on the field, can be taken into account, as well as external driving forces on both the cavity and the wall. The model exactly reproduces the resonant cavity mode stimulation due to the periodic motion of the mirror (dynamical Casimir effect), as well…
We consider the scenario in which a damped three-level atom in the ladder or V configurations is coupled to a single cavity mode whose vacuum state is amplified by dint of the dynamical Casimir effect. We obtain approximate analytical expressions and exact numerical results for the time-dependent probabilities, demonstrating that the presence of the third level modifies the photon statistics and its population can serve as a witness of photon generation from vacuum.
Two different quantum processes are considered in a perturbed vacuum cavity: time refraction and dynamical Casimir effect. They are shown to be physically equivalent, and are predicted to be unstable, leading to an exponential growth in the number of photons created in the cavity. The concept of an effective Unruh acceleration for these processes is also introduced, in order to make a comparison in terms of radiation efficiency, with the Unruh radiation associated with an accelerated frame in unbounded vacuum.
We demonstrate that a very recently obtained formula for the force on a slab in a material planar cavity based on the calculation of the vacuum Lorentz force [C. Raabe and D.-G. Welsch, Phys. Rev. A 71, 013814 (2005)] describes a (medium) screened Casimir force and, in addition to it, a medium-assisted force. The latter force also describes the force on the cavity medium. For dilute media, it implies the atom-mirror interaction of the Casimir-Polder type at large and of the Coulomb type at small atom-mirror distances of which the sign is insensitive to the polarizability type (electric or magn…
We present a full analysis of the mode spectrum in a cavity formed by two parallel plates, one of which is a magneto-dielectric, e.g. a metamaterial, while the other one is metallic, and obtain dispersion relations in closed form. The optical properties of the cavity walls are described in terms of realistic models for the effective permittivity and the permeability. Surface polaritons, i.e. electromagnetic modes that have at least partly an evanescent character, are shown to dominate the Casimir interaction at small separations. We analyze in detail the s-polarized polaritons, which are a cha…
Finding strategies to preserve quantum resources in open systems is nowadays a main requirement for reliable quantum-enhanced technologies. We address this issue by considering structured cavities embedding qubits driven by a control technique known as frequency modulation. We first study a single qubit in a lossy cavity to determine optimal modulation parameters and qubit-cavity coupling regime allowing a gain of four orders of magnitude concerning coherence lifetimes. We relate this behavior to the inhibition of the qubit effective decay rate rather than to stronger memory effects (non-Marko…
We investigate the electromagnetic Casimir interactions of an object contained within an otherwise empty, perfectly conducting spherical shell. For a small object we present analytical calculations of the force, which is directed away from the center of the cavity, and the torque, which tends to align the object opposite to the preferred alignment outside the cavity. For a perfectly conducting sphere as the interior object, we compute the corrections to the proximity force approximation (PFA) numerically. In both cases the results for the interior configuration match smoothly onto those for th…
We show two examples in which the dynamical Casimir effect can be achieved by modulating the Kerr or higher order nonlinearities. In the first case the cavity field is coupled to an arbitrary number of qubits or an harmonic oscillator via the dipole interaction. In the second case, the modulation of the nonlinearities is accompanied by the off-resonance modulation of the cavity frequency. We present the analytic description of the phenomenon and supplement it with numeric simulations, demonstrating that photons can be created from vacuum and the resulting hyper-Poissonian photon statistics is …
We consider the vacuum-field pressure on boundaries of a metal slab in the middle of a cavity with perfectly reflecting mirrors adopting the plasma model for the metal and paying special attention to the surface plasmon polariton contribution to the pressure. We demonstrate that, with increasing cavity length, the pressure on a thin (d<<λ_P) slab in this system decreases from the Casimir pressure F_C at zero slab-mirror distances to the non-retarded force per unit area F_nr=1.19 (d/λ_P)F_C in the case of an isolated slab. In the first case the pressure is entirely due to the photonic modes pro…
Two two-level atoms within a leaky optical cavity is driven by two independent external optical white noise fields. We investigate how entanglement between two atoms arises in such a situation. The steady state entanglement of two atoms is also investigated. A stochastic-resonance-like behavior of entanglement is revealed. Finally, the Bell violation between atoms is discussed.
